On Scalable Testing of Samplers

TL;DR

This paper introduces a significantly faster algorithm for testing high-dimensional constrained samplers, reducing query complexity from exponential to linear in the dimension, enabling practical scalability in safety-critical ML applications.

Contribution

The paper presents an exponentially faster testing algorithm for constrained samplers with linear query complexity, improving scalability over previous methods.

Findings

The new algorithm requires 10x fewer samples for wUnigen3.

It requires 450x fewer samples for wSTS.

Experimental results demonstrate practical efficiency gains.

Abstract

In this paper we study the problem of testing of constrained samplers over high-dimensional distributions with $(\varepsilon,\eta,\delta)$ guarantees. Samplers are increasingly used in a wide range of safety-critical ML applications, and hence the testing problem has gained importance. For $n$-dimensional distributions, the existing state-of-the-art algorithm, $\mathsf{Barbarik2}$, has a worst case query complexity of exponential in $n$ and hence is not ideal for use in practice. Our primary contribution is an exponentially faster algorithm that has a query complexity linear in $n$ and hence can easily scale to larger instances. We demonstrate our claim by implementing our algorithm and then comparing it against $\mathsf{Barbarik2}$. Our experiments on the samplers $\mathsf{wUnigen3}$ and $\mathsf{wSTS}$, find that $\mathsf{Barbarik3}$ requires $10\times$ fewer samples for $\mathsf{wUnigen3}$ and $450\times$ fewer samples for $\mathsf{wSTS}$ as compared to $\mathsf{Barbarik2}$.